Factorise this quadratic = 8x^2 + 2x -3

As the coefficient of x^2 is not 1, we think of this equation as ax^2 +bx + c. When the coefficient of x^2 is not 1, then we need to firstly multiply the first and last numbers together (8 and -3) which gives us -24. Then we look at b which is 2. Then we need to think of two numbers that multiply to make -24 and add together to make 2. This would be 6 and -4. You then break up b into these two coefficients giving 8x^2 -4x +6x -3. Then split this into two brackets. (8x^2 -4x) PLUS ( +6x -3). Then factorise further within these two . The first part would go to 4x(2x-1) and the second part would go to 3(2x-1). The parts in brackets should be the same. Therefore, take this out as a factor; (2x-1) (4x+3). Always expand out at the end to double check!